Peel, rinse, and slice the potatoes-Cut them in half length, and then again in quarters.
Pour the oil in a frying pan, and while the oil is getting hot, we will cut the potatoes, and chop the onions.

Add the potatoes to the pan, and fry the potatoes for a few minutes before adding the onions. Stir occasionally until the potatoes are softened. Cooking times will depend on the thickness of the potatoes.

Once the potatoes are cooked, strain the potatoes, and onions through a colander into a large bowl or a plate with kitchen paper towel to remove excess of oil.
Beat the eggs separately.
Stir the eggs into the potatoes.
Add salt and pepper- You can also add fresh chopped parsley.

Get a few spoons of the strained oil, and heat it in a smaller frying pan.

Place the eggs ,and potatoes mixture into the pan, and cook on a low-moderate heat while using a spatula to shape the omelette into a compact cushion.

When you notice that the omelette is almost set, invert it on a plate, and slide it back into the frying pan. Once in the pan, press the edges to shape the omelette.

Repeat this process until the omelette looks to your liking.
Note: Some people likes to cook their omelette just a few minutes just so the eggs are fully cooked on the outside while still runny on the inside. As you can see by looking at the pictures, I personally like mine well done. I usually press the tortilla with a spatula, and if I see tiny "oil bubbles"around the edges, that means the tortilla is not fully cooked in the inside. You will know it is fully cooked by the firmness of the tortilla, and the absence of "oil bubbles"